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My experience with students and math is that it is often the feared subject area. Word problems of any kind are typicallty impossible for some to figure out without some guidance.

At each, grade 10 and 11, I have a course that is entirely word problem-based (Workplace and apprenticeship math) , and one that is not (Foundations for pre-calculus). I found that students in the workplace math initially struggled with the wording. They need to know what is being asked of them before they can even attempt to do the calculation. I had to spend several weeks to get students understanding the language of math or else the problems would be gibberishand they would get the calculation wrong -not something you want your future carpenter or architect to be doing,

The simple problem you mentionedin the post, was very likely what Ken said, a stepping stone. Students need to become more familiar with the language of mathematics so that they can succeed at it. Every great mathematician has to start somewhere.

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Looked at one way, a math problem is a puzzle. I think that is why I enjoyed math.

I see also they threw unnecessary information at you, to make the puzzle tougher. ie, first you have to sort through the noise to discover the need to do 5 * 5 or 5 / 1/5.

Come to think of it, my uncertainty may be the point: how do we get from (somewhat) natural language to the arithmetic? A valid CCSS concern is the many kids who can do procedural math out the wazoo but come up empty on word problems (meaning they cannot really use math in the real world — they do not even know what to bang into a calculator when they have one).

I taught eighth grade math and had them doing great on procedural math. Then came the bit on word problems. Not only was it a disaster, but I could not even figure out how to help them make that leap.

Perhaps word problems like these where the natural language is quite close to being straight arithmetic are a stepping stone?

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